How Bright is a Firefly? Resolving a Century of Overestimation

“How Bright is a Firefly?”
by David Silver.

My favorite science journal is the American Journal of Physics. I was browsing through recent issues and found a lovely article by David Silver titled “How bright is a firefly? Resolving a century of overestimation” (Volume 94, Pages 520–524, July, 2026). The abstract is given below.

A firefly flash contains roughly 10⁸–10¹¹ photons—far fewer than the 10¹³–10¹⁴ photons implied by Coblentz’s 1912 report of 1/50–1/400 candlepower for Photinus pyralis. We trace this discrepancy to selective citation of the upper end of Coblentz’s range and to systematic biases in early visual photometry. We derive a theoretical bound from luciferase abundance and quantum yield. We also measure flash brightness directly with a lux meter and reanalyze two historical datasets. These independent lines of evidence all fall well below the historical candlepower values. The error persisted because modern bioluminescence research often reports quantum yields and relative intensities; reconstructing absolute photons per flash also requires in vivo substrate turnover or measurement geometry, so the comparison with early photometry was rarely made directly.

What did I like about this paper?

1. I’m fascinated by how errors propagate through the scientific literature. Not little mistakes, but orders-of-magnitude blunders in determining the value of physical parameters. In this case, there seems to be a thousand-fold difference between the commonly reported value for the number of photons emitted by a firefly flash and the actual number of photons. How can researchers get something that wrong? It reminds me of the motto I repeatedly urged my undergraduate physics students to adopt: “Think before you calculate!” Scientists need to make order-of-magnitude estimates, like those in this article, before doing more detailed calculations and even before making extensive measurements.
2. My wife and I are native plant gardeners. Our goal is to attract and support pollinators, but one side benefit is that we encourage fireflies. Back when I was growing up in Morrison, Illinois, we called them lightning bugs. During summer nights their flashing lights filled our back yard. We used to catch some, put them in a glass jar, and bring them with us to our bedroom to serve as a nightlight. Nowadays there are far fewer lightning bugs, at least in the subdivision where I live in Michigan. Any physics article about lightning bugs is going to interest me.
3. The article uses both radiometry and photometry units. Intermediate Physics for Medicine and Biology has a long section about these different units. Radiometric quantities are in traditional metric units. For example, the radiant flux (power emitted) is in watts. Photometric quantities weight the light emitted by the sensitivity of the eye. For green light, one watt corresponds to 683 lumens, where the lumen is the photometric unit. The same one watt emitted in the infrared or ultraviolet would have zero lumens.
4. I learned a new unit! First, let me describe a photometric unit I was already familiar with, the candela. One lumen per steradian (solid angle) is one candela. The luminance, or luminance intensity, is the number of candelas per square meter. The unit that I had never heard of is the lambert. The lambert is one over π candelas per square meter. Why the 1/π? I expect it has something to do with the solid angle, but I’m not sure.
5. It is often useful to translate these units into number of photons. The lumen measures the number of photons emitted per second. The candela is the number of photons per steradian. The lambert is the number of photons per steradian per square meter (with that pesky 1/π thrown in). If you’re interested in the total number of photons per steradian per square meter recorded by a single flash of the firefly at some distance from the bug, the lambert is the unit you want. If you can assume the light is emitted isotropically, the solid angle is just a factor of 4π. The per m² accounts for the 1/r²  fall off of the intensity. 
6. So who is Lambert? Johann Heinrich Lambert (1728–1777) was a Swiss mathematician, physicist, and astronomer. This is the same Lambert of Lambert’s cosine law discussed in Section 14.12 of IPMB. This is also the same guy as in the Beer-Lambert law introduced in Section 14.5. Asinov’s Biographical Encyclopedia of Science & Technology states: “In 1760 he [Lambert] published his investigations of light reflection. His book was in Latin and his word for the fraction of light reflected diffusely by a body was albedo (“whiteness”). The term is still commonly used in astronomy to represent the reflectivity of planetary bodies. He was the first to devise methods for measuring light intensities accurately, and the unit of brightness is the lambert, in his honor.”

Asimov's Biographical Encyclopedia of Science & Technology.